Solve for x 4x^(3/2)=32

$4 x^{\frac{3}{2}} = 32$

Divide each term in $4 x^{\frac{3}{2}} = 32$ by $4$ and simplify.

Divide each term in $4 x^{\frac{3}{2}} = 32$ by $4$ .

$\frac{4 x^{\frac{3}{2}}}{4} = \frac{32}{4}$

Simplify the left side.

Cancel the common factor.

$\frac{4 x^{\frac{3}{2}}}{4} = \frac{32}{4}$

Divide $x^{\frac{3}{2}}$ by $1$ .

$x^{\frac{3}{2}} = \frac{32}{4}$

Simplify the right side.

Divide $32$ by $4$ .

$x^{\frac{3}{2}} = 8$

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{3}{2}})}^{\frac{2}{3}} = 8^{\frac{2}{3}}$

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Multiply the exponents in ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 8^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 8^{\frac{2}{3}}$

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 8^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 8^{\frac{2}{3}}$

Rewrite the expression.

$x^{1} = 8^{\frac{2}{3}}$

Simplify.

$x = 8^{\frac{2}{3}}$

Simplify the right side.

Simplify $8^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

$x = {(2^{3})}^{\frac{2}{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = 2^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = 2^{3 (\frac{2}{3})}$

Rewrite the expression.

$x = 2^{2}$

Raise $2$ to the power of $2$ .

$x = 4$

Solve for x 4x^(3/2)=32

Related Questions

Support LCMGCF.com by disabling your adblocker.